In QAM, two carrier signals in phase quadrature are amplitude modulated by modulating signals, and are subsequently combined for example for transmission in a microwave radio transmission system. Each transmitted symbol can thus have any one of a relatively large number of phase and amplitude states, which are generally illustrated as signal points in a signal point constellation in a phase plane diagram. Various signal point constellations, of triangular, rectangular, circular, and hexagonal forms and for various numbers of signal points, are described for example in "Digital Amplitude-Phase Keying with M-ary Alphabets" by C. Melvil Thomas et al., presented at the 1972 International Telemetry Conference, Los Angeles, Calif.
For digital transmission of binary data signals, it is convenient for the number of signal points in the signal point constellation to be an integral power of 2. Thus for example 64-QAM transmission systems, in which there are 64 signal points in the constellation so that each transmitted symbol can represent 6 bits (2.sup.6 =64), are well known. With increasing demands for data transmission, and increasingly more sophisticated techniques, it is desirable to provide higher numbers of signal points in the constellation. Accordingly, 256-QAM transmission systems, in which each transmitted symbol represents 8 bits (2.sup.8 =256), have been proposed.
It is well known that the signal points should be spaced in the phase plane as far apart as possible to provide the greatest possible signal-to-noise (S/N) ratio, and that the signal points should have the smallest possible amplitudes to minimize the peak power of the transmitted signal. It is also desirable to simplify as far as possible the coding and decoding circuitry required for converting between the signal points in the phase plane and the digital signals which they represent. Particularly in view of this last matter, rectangular signal point constellations, in which the signal points are arranged on a rectangular matrix or grid, have been preferred. Where the number of signal points is an even power of 2, the signal point constellation becomes a square array, for example of 16 by 16 signal points for 256-QAM.
A problem with a square array of 256 signal points is that the points at the corners of the square have relatively large amplitudes, and hence result in a high peak power and a high peak-to-average power ratio for the transmitted signal. In order to reduce this problem, it is known for example from Uchibori et al. U.S. Pat. No. 4,675,619 dated June 23, 1987 and entitled "Multiple Quadrature-Phase Amplitude Modulating System Capable of Reducing a Peak Amplitude" to provide a modified, or stepped, square 256-QAM signal point constellation in which the peak amplitude is reduced, relative to a square constellation, by relocating 6 signal points from each corner of a 16 by 16 point square so that the signal points are arranged in an extrapolated square matrix within a generally circular pattern. While this relocation of signal points results in reduced peak amplitudes, it introduces a further disadvantage, discussed below.
More specifically, Gray coding of digital input signals is generally used so that the digital signal represented by each signal point in the constellation differs from the digital signal represented by any immediately adjacent signal point in only one bit position. Thus a transmitted symbol or signal point which is corrupted and consequently interpreted mistakenly as an adjacent signal point contains only a single bit error. Such a single bit error can be relatively easily detected and corrected using known FEC (forward error correction) coding schemes; for example, a (511,493) BCH code can be used which can correct up to two bits in error in a block of 511 bits, with a resulting increase in the transmitted bit rate of about 3.6%.
However, relocating signal points in the manner discussed above results in 32 of the 256 signal points representing digital signals having 3 bits different from the signal represented by an immediately adjacent signal point; in other words they have a Hamming distance of 3 rather than the preferred Hamming distance of 1. Corruption and consequent misinterpretation of such a signal point results in 3 bits being in error, and this is not correctable using the (511,493) BCH code discussed above.
In order to reduce this and other disadvantages, in Kennard et al. U.S. Pat. No. 4,855,692 issued Aug. 8, 1989 and entitled "Method of Quadrature Phase Modulation", the entire disclosure of which is hereby incorporated herein by reference, there is described and claimed a modified square QAM transmission system in which the relocation of signal points is effected in a manner to minimize the adverse effects of transmission errors.
It is becoming increasingly desirable for microwave radio transmission channels, which have bandwidths of nominally 20, 30, or 40 MHz for the various microwave radio bands at frequencies of the order of 4, 6, and 11 GHz, to accommodate standardized forms of signals for transmission. One of the currently most significant standardized signal forms is SONET, in which signals, referred to as STS-N signals where N is an integer having preferred values of 1, 3, 9, 12, etc., have bit rates of N times 51.84 Mb/s. In particular, a so-called STS-3 SONET signal has a bit rate of 155.52 Mb/s.
Unfortunately, using 256-QAM with FEC, and allowing for necessary channel filter roll-offs, these microwave channel bandwidths provide a poor and inefficient match for the bit rates of SONET signals. For example, a 256-QAM 40 MHz channel provides a transmission rate which is a little less than that required for two STS-3 signals. Accommodating only one STS-3 signal on such a channel would be very inefficient, and accommodating one STS-3 signal together with other, e.g. two STS-1, signals would result in undesired complexity.
In order to avoid this problem, it is desirable to use a modulation scheme which provides a more convenient and efficient matching of microwave radio transmission channels to SONET transmission rates. In particular, a 512-QAM modulation scheme enables this to be done. For example, the use of 512-QAM enables one STS-3 signal to be carried by a 20 MHz channel, and two STS-3 signals to be carried by a 40 MHz channel, in a convenient and relatively efficient manner.
However, the use of 512-QAM means that the techniques discussed above, relating to modifying a square signal point constellation to make it nearly circular, can no longer be used because 512 is an odd, not an even, power of 2.
For QAM signal point constellations with an odd power of 2 points, e.g. with 32 or 128 signal points, it is known to use a or cross arrangement of the signal points to reduce peak amplitudes. For example, such arrangements are described in the paper by Thomas et al. referred to above, and in a companion paper by J. G. Smith entitled "Odd-Bit Quadrature Amplitude-Shift Keying", presented at the 1974 International Telemetry Conference, Los Angeles, Calif. The latter paper also describes a rectangular block signal point constellation. In either case, however, the peak amplitude for a constellation of 512 signal points is undersirably high.
An object of this invention, therefore, is to provide an improved QAM method in which the above disadvantages are reduced or avoided.